Average Error: 58.1 → 58.1
Time: 1.1m
Precision: 64
Internal precision: 128
\[\left(\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
⬇
\[\frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\frac{\left(\left(\left({-2}^{3} + {\left({33096}^{4} \cdot -121\right)}^{3}\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right) + \left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left({\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2\right)\right) \cdot {77617}^2\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)\right) + \left(\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}\right)}{\left(\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)\right)}}{1} - \frac{77617}{33096 + 33096}}\]

Error

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
  2. Using strategy rm

  3. Applied flip-+ 58.1

    \[\leadsto \color{blue}{\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}} + \frac{77617}{2 \cdot 33096}\]
  4. Using strategy rm

  5. Applied flip-+ 58.1

    \[\leadsto \color{blue}{\frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} - \frac{77617}{2 \cdot 33096}}}\]

  6. Applied simplify 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\color{blue}{\frac{\left(\left(-2 + {33096}^{4} \cdot -121\right) + \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 + \left(-{33096}^{6}\right)\right)\right) \cdot {77617}^2 + \left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right)}{1} - \frac{77617}{33096 + 33096}}}\]
  7. Using strategy rm

  8. Applied flip3-+ 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\left(\left(-2 + {33096}^{4} \cdot -121\right) + \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 + \left(-{33096}^{6}\right)\right)\right) \cdot {77617}^2 + \color{blue}{\frac{{\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}}{{\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)}}}{1} - \frac{77617}{33096 + 33096}}\]

  9. Applied flip-+ 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\left(\left(-2 + {33096}^{4} \cdot -121\right) + \color{blue}{\frac{{\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2}{\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)}}\right) \cdot {77617}^2 + \frac{{\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}}{{\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)}}{1} - \frac{77617}{33096 + 33096}}\]

  10. Applied flip3-+ 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\left(\color{blue}{\frac{{-2}^{3} + {\left({33096}^{4} \cdot -121\right)}^{3}}{{-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)}} + \frac{{\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2}{\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)}\right) \cdot {77617}^2 + \frac{{\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}}{{\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)}}{1} - \frac{77617}{33096 + 33096}}\]

  11. Applied frac-add 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\color{blue}{\frac{\left({-2}^{3} + {\left({33096}^{4} \cdot -121\right)}^{3}\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right) + \left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left({\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2\right)}{\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)}} \cdot {77617}^2 + \frac{{\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}}{{\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)}}{1} - \frac{77617}{33096 + 33096}}\]

  12. Applied associate-*l/ 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\color{blue}{\frac{\left(\left({-2}^{3} + {\left({33096}^{4} \cdot -121\right)}^{3}\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right) + \left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left({\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2\right)\right) \cdot {77617}^2}{\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)}} + \frac{{\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}}{{\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)}}{1} - \frac{77617}{33096 + 33096}}\]

  13. Applied frac-add 58.1

    \[\leadsto \frac{{\left(\frac{{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}}\right)}^2 - {\left(\frac{77617}{2 \cdot 33096}\right)}^2}{\frac{\color{blue}{\frac{\left(\left(\left({-2}^{3} + {\left({33096}^{4} \cdot -121\right)}^{3}\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right) + \left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left({\left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2\right)}^2 - {\left(-{33096}^{6}\right)}^2\right)\right) \cdot {77617}^2\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)\right) + \left(\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^{3} + {\left({33096}^{8} \cdot 5.5\right)}^{3}\right)}{\left(\left({-2}^2 + \left({\left({33096}^{4} \cdot -121\right)}^2 - -2 \cdot \left({33096}^{4} \cdot -121\right)\right)\right) \cdot \left(\left({33096}^2 \cdot 11\right) \cdot {77617}^2 - \left(-{33096}^{6}\right)\right)\right) \cdot \left({\left(333.75 \cdot {33096}^{6}\right)}^2 + \left({\left({33096}^{8} \cdot 5.5\right)}^2 - \left(333.75 \cdot {33096}^{6}\right) \cdot \left({33096}^{8} \cdot 5.5\right)\right)\right)}}}{1} - \frac{77617}{33096 + 33096}}\]
  14. Removed slow pow expressions

Runtime

Time bar (total: 1.1m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(445090408 2096966519 1102989176 1729990921 3285957378 3536114456)'
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (sqr 77617) (+ (+ (+ (* (* 11 (sqr 77617)) (sqr 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))